Heretofore, known speed control apparatus for elevators which utilize an induction motor for driving a cage commonly employ variable voltage and variable frequency speed control of the induction motor (hereinbelow, termed "V.V.V.F. control"). In this apparatus slip frequency control is used as a basis for the V.V.V.F. control of the induction motor. However, such apparatus has been known to have problems in operating an elevator smoothly without causing sudden abrupt movements during the elevator starting operation.